不可分解全自反模的不可数无穷个数
An uncountably infinite number of indecomposable totally reflexive modules
摘要：
几年前，Huneke和Leuschke证明了一个定理，解决了Schreyer的一个猜想。证明了可数Cohen-Macaulay型的完备或具有不可数剩余域的优良Cohen-Macaulay局部环至多有一个一维奇异轨迹.本文证明了这一定理的优良性质的假设是可以去掉的，并在任意的局部环上讨论了这一定理。本文的主要目的是证明某个素理想和某个全自反模的存在蕴含着不可分解的全自反模的同构类的不可数无穷个的存在性。
英文摘要：
A few years ago, Huneke and Leuschke proved a theorem which solved a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
